if( !require('NLRoot') ){
    install.packages('NLRoot')
}
library(NLRoot)

# Plot the region where the argument of the square root is positive:
# 
x = seq( -4, 5.5, length.out=500 )
y = function(x){ 13 + 4*x^3 - 4*exp(x) }
ys = y(x) 
plot( x, ys, type='l' )
abline(h=0, col='blue')
grid()

BFfzero( y, -2.0, 0 )
BFfzero( y, 4.0, 5.0 )

#postscript("../../WriteUp/Graphics/Chapter2/chap_2_sect_2_prob_17_plot.eps", onefile=FALSE, horizontal=FALSE)

x = seq( -1.43, 4.6, length.out=100 )
y = function(x){ ( 5 - sqrt( 13 + 4*x^3 - 4*exp(x) ) )/2 }
ys = y(x) 
plot( x, ys, type='l', xlab='x', ylab='y(x)' )
grid()

#dev.off()